Inverse of matrix

Q.

What is an inverse in matrix?

Q. If $A=\left[\begin{array}{cc}2x& 0\\ x& x\end{array}\right]$ and $A^{-1}=\left[\begin{array}{cc}1& 0\\ -1& 2\end{array}\right]$ then the value of $x$ is

1. 1
2. 2
3. $\frac{1}{2}$
4. None

Q. Let $A=\left[\begin{array}{cc}2& -0.1\\ 0& 3\end{array}\right]$ and $A^{-1}=\left[\begin{array}{cc}\frac{1}{2}& a\\ 0& b\end{array}\right]$. Then $(a+b)=$

1. $\frac{7}{20}$
2. $\frac{3}{20}$
3. $\frac{19}{60}$
4. $\frac{11}{20}$

Q.

Find it using identity.

${\left(104\right)}^3$

Q. Let A be an invertible matrix and suppose that the inverse of A is $\left[\begin{array}{cc}-1& 2\\ 4& -7\end{array}\right]$. Then the matrix A is

1. $\left[\begin{array}{cc}1& \frac{2}{7}\\ \frac{4}{7}& \frac{1}{7}\end{array}\right]$
2. $\left[\begin{array}{cc}7& 2\\ 4& 1\end{array}\right]$
3. $\left[\begin{array}{cc}1& \frac{-4}{7}\\ \frac{-2}{7}& \frac{1}{7}\end{array}\right]$
4. $\left[\begin{array}{cc}7& 4\\ 2& 1\end{array}\right]$

Q. The inverse of the $2\times 2$ matrix $\left[\begin{array}{cc}2& 3\\ 6& 8\end{array}\right]$ is

1. $\left[\begin{array}{cc}3& -1\\ -4& \frac{3}{2}\end{array}\right]$
2. $\left[\begin{array}{cc}-4& \frac{3}{2}\\ 3& -1\end{array}\right]$
3. $\left[\begin{array}{cc}6& -2\\ -8& 3\end{array}\right]$
4. $\left[\begin{array}{cc}4& -\frac{3}{2}\\ -3& 1\end{array}\right]$

Q. Let A, B , C, D be n$\times$ n matrices, each with non zero determinant and ABCD = I then $B^{-1}=$

1. $D^{-1}{C}^{-1}{A}^{-1}$
2. CDA
3. ABC
4. Does not exist

Q. The inverse of the matrix $\left[\begin{array}{cc}3+2i& i\\ -i& 3-2i\end{array}\right]$ is

1. $\frac{1}{12}$ $\left[\begin{array}{cc}3+2i& -i\\ i& 3-2i\end{array}\right]$
2. $\frac{1}{12}$ $\left[\begin{array}{cc}3-2i& -i\\ i& 3+2i\end{array}\right]$
3. $\frac{1}{14}$ $\left[\begin{array}{cc}3+2i& -i\\ i& 3-2i\end{array}\right]$
4. $\frac{1}{14}$ $\left[\begin{array}{cc}3-2i& -i\\ i& 3+2i\end{array}\right]$

Q. Inverse of matrix$\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 1& 0& 0\end{array}\right]$ is

1. $\left[\begin{array}{ccc}0& 0& 1\\ 1& 0& 0\\ 0& 1& 0\end{array}\right]$
2. $\left[\begin{array}{ccc}1& 0& 0\\ 0& 0& 1\\ 0& 1& 0\end{array}\right]$
3. $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$
4. $\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right]$

Q. For a given matrix $P=\left[\begin{array}{cc}4+3i& -i\\ i& 4-3i\end{array}\right]$, $i=\sqrt{-}1$, the inverse of matrix P is

1. $\frac{1}{24}$$\left[\begin{array}{cc}4-3i& i\\ -i& 4+3i\end{array}\right]$
2. $\frac{1}{25}$$\left[\begin{array}{cc}i& 4-3i\\ 4+3i& -i\end{array}\right]$
3. $\frac{1}{24}$$\left[\begin{array}{cc}4+3i& -i\\ i& 4-3i\end{array}\right]$
4. $\frac{1}{25}$$\left[\begin{array}{cc}4+3i& -i\\ i& 4-3i\end{array}\right]$
   

Q. Let A be an invertible matrix and suppose that the inverse of A is $\left[\begin{array}{cc}-1& 2\\ 4& -7\end{array}\right]$. Then the matrix A is

1. $\left[\begin{array}{cc}1& \frac{2}{7}\\ \frac{4}{7}& \frac{1}{7}\end{array}\right]$
2. $\left[\begin{array}{cc}7& 2\\ 4& 1\end{array}\right]$
3. $\left[\begin{array}{cc}1& \frac{-4}{7}\\ \frac{-2}{7}& \frac{1}{7}\end{array}\right]$
4. $\left[\begin{array}{cc}7& 4\\ 2& 1\end{array}\right]$

Q. If P, Q, R & S are non singular matrix of order three such that PQRS = I then $R^{-1}$ is

1. PQS
2. QPS
3. SPQ
4. PSQ

Q. The inverse of the matrix $A=\left[\begin{array}{cc}-3& 5\\ 2& 1\end{array}\right]$ is

1. $\left[\begin{array}{cc}\frac{5}{13}& \frac{-1}{13}\\ \frac{2}{13}& \frac{3}{13}\end{array}\right]$
2. $\left[\begin{array}{cc}\frac{2}{13}& \frac{5}{13}\\ \frac{-1}{13}& \frac{3}{13}\end{array}\right]$
3. $\left[\begin{array}{cc}\frac{-1}{13}& \frac{5}{13}\\ \frac{2}{13}& \frac{3}{13}\end{array}\right]$
4. $\left[\begin{array}{cc}\frac{1}{13}& \frac{-5}{13}\\ \frac{2}{13}& \frac{3}{13}\end{array}\right]$
   

Q. The inverse of matrixis? $\left|\begin{array}{ccc}1& 0& 1\\ -1& 1& 1\\ 0& 1& 0\end{array}\right|$

Q. The inverse of the matrix
$S=\left[\begin{array}{ccc}1& -1& 0\\ 1& 1& 1\\ 0& 0& 1\end{array}\right]\text{is}$

1. $\left[\begin{array}{ccc}1& 0& 1\\ 0& 0& 0\\ 0& 1& 1\end{array}\right]$
2. $\left[\begin{array}{ccc}0& 1& 1\\ -1& -1& 1\\ 1& 0& 1\end{array}\right]$
3. $\left[\begin{array}{ccc}2& 2& -2\\ -2& 2& -2\\ 0& 2& 2\end{array}\right]$
4. $\left[\begin{array}{ccc}\frac{1}{2}& \frac{1}{2}& \frac{-1}{2}\\ \frac{-1}{2}& \frac{1}{2}& \frac{-1}{2}\\ 0& 0& 1\end{array}\right]$
   

Q. For a given matrix $P=\left[\begin{array}{cc}4+3i& -i\\ i& 4-3i\end{array}\right]$, $i=\sqrt{-}1$, the inverse of matrix P is

1. $\frac{1}{24}$$\left[\begin{array}{cc}4-3i& i\\ -i& 4+3i\end{array}\right]$
2. $\frac{1}{25}$$\left[\begin{array}{cc}i& 4-3i\\ 4+3i& -i\end{array}\right]$
3. $\frac{1}{24}$$\left[\begin{array}{cc}4+3i& -i\\ i& 4-3i\end{array}\right]$
4. $\frac{1}{25}$$\left[\begin{array}{cc}4+3i& -i\\ i& 4-3i\end{array}\right]$
   

Q.

How do you factor $a^3-b^3$?

Q. The matix $\left|\begin{array}{cc}1& -4\\ 1& -5\end{array}\right|$ is an inverse of the matix

1. Ture
2. False

Q. Let $M^4=I$, (Where i denotes the identity matrix) and $M\ne I$ and $M^2\ne I$ and $M^3\ne I.$ Then, for any natural number k, $K^{-1}$ equals:

1. $M^{4k+1}$
2. $M^{4k+2}$
   
3. $M^{4k+3}$
   
4. $M^{4k}$
   

Q.

Simplify the following : ${\left(104\right)}^2$

Q. If $A=\left[\begin{array}{ccc}5& 0& 2\\ 0& 3& 0\\ 2& 0& 1\end{array}\right],then{A}^{-1}=$

1. $\left[\begin{array}{ccc}1& 0& -2\\ 0& \frac{1}{3}& 0\\ -2& 0& 5\end{array}\right]$
2. $\left[\begin{array}{ccc}5& 0& 2\\ 0& -\frac{1}{3}& 0\\ 2& 0& 1\end{array}\right]$
3. $\left[\begin{array}{ccc}\frac{1}{5}& 0& \frac{1}{2}\\ 0& \frac{1}{3}& 0\\ \frac{1}{2}& 0& 1\end{array}\right]$
4. $\left[\begin{array}{ccc}\frac{1}{5}& 0& -\frac{1}{2}\\ 0& \frac{1}{3}& 0\\ -\frac{1}{2}& 0& 1\end{array}\right]$

Q.

Simplify the following: ${\left(96\right)}^2$